It also criticised the pay-offs given to 10 other senior managers, including £949,000 for former deputy director-general Mark Byford and £670,000 for former chief operating officer Caroline Thomson.

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During a PAC session, MPs claimed Ms Thomson had been awarded the money partly as "compensation" after she missed out on the job of director-general.

The committee's report described the payments as "excessively generous" and also expressed concern that the BBC Trust had turned down an offer from the National Audit Office to examine its deal with Mr Entwistle.

Ms Hodge said: "The BBC's generosity with severance packages goes beyond the one awarded to George Entwistle. Since 2010, over £4m in total has been made in severance payments to 10 other departing senior managers.

"The BBC is also providing 422 senior managers with private medical cover as part of their remuneration packages.

"We have asked the comptroller and auditor general to include in his 2013 programme of work on the BBC an examination of severance payments and benefits for senior managers."

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Mr Entwistle was only due £225,000 under his contract but demanded more. A deal was quickly signed off to allow a clean break and the appointment of a new boss as soon as possible.

The committee said: "By agreeing to this payment, the BBC Trust may have secured the director-general's quick departure but it did not act in the wider public interest. Public servants should not be rewarded for failure."

The Trust insists the terms were the "best available in the circumstances" because a legal battle had they refused would have taken time and could have cost even more.

Lord Patten told BBC's Radio 4 Today programme: "It was precisely because we were dealing with public money and a great public service broadcaster that we took the view that it was more sensible to settle for the amount that we were being asked for rather than fetch up paying more for a constructive dismissal."

He added: "We've taken legal advice about whether we could actually take any money back. In order for us to do so we have to be able to argue that, on the basis of what Pollard says, it would have been justified to make a summary dismissal of the former director-general.

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"I rather doubt whether we will get the legal go ahead for that."

But Ms Hodge said: "They don't get it that they are being paid through the licence fee, which is a form of taxation, and they don't understand that people find this astonishing."